General Relativity and Black Holes - Guided Notes update
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Guided Notes – General Relativity and Black Holes
Name:
Leah Walker
These notes cover Part IV of
Video Lecture – Stellar Evolution
.
Please type or handwrite notes as you watch the video lecture and answer the
included questions.
General Relativity:
General relativity is a theory by Albert Einstein that describes gravity as a property of space and time. It
refines Newton's law of universal gravitation and is essential in understanding astronomical objects like
black holes. When a massive star's core collapses under its weight, it creates a black hole.
Black Holes:
A black hole is a region where gravity is so strong that nothing can escape it, not even light. The core of a
massive star collapses and if its mass is more than three times that of the Sun, it collapses forever. This
creates a black hole, which is invisible but can be inferred through its interaction with other matter and
radiation.
Your Turn: Schwarzschild Radius
Calculate the Schwarzschild radius for the planet Jupiter, with a mass that is 1000 times smaller than the
Sun.
Your answer:
r_s = 2GM/c^2
G = 6.674 x 10^-11 m^3 kg^-1 s^-2),
c = 3 x 10^8 m/s).
M_jupiter = M_sun / 1000
M_jupiter = 1.989 x 10^30 kg / 1000
M_jupiter = 1.989 x 10^27 kg
r_s = 2 * (6.674 x 10^-11 m^3 kg^-1 s^-2) * (1.989 x 10^27 kg) / (3 x 10^8 m/s)^2
r_s = 2 * (6.674 x 10^-11 m^3 kg^-1 s^-2) * (1.989 x 10^27 kg) / 9 x 10^16 m^2/s^2
r_s = 2.95 meters
Detecting Black holes:
Black holes are detected by observing their effects on surrounding matter. This can
be done by studying the X-rays emitted from their accretion disks, observing the
motion of stars and gas, and studying the behavior of surrounding objects.
Test Yourself: Black Hole X-Rays
At first it was always thought that nothing could escape from a black hole, yet astronomers are locating
black hole candidates by the X rays they emit. Why do they see X rays coming from a black hole?
a) The X rays come from highly compressed matter in the accretion disk outside the event horizon of the
black hole.
b) The black hole modifies spacetime around it so much that particles and X rays are created in the
vacuum itself, just outside the event horizon.
c) The X rays are produced by vibrations of the black hole itself, and therefore they come from the event
horizon, and not from inside the black hole.
d) X rays are not light or matter, therefore they can escape from inside the black hole.
Your answer:
a) The X rays come from highly compressed matter in the accretion disk outside the event
horizon of the black hole.
Test Yourself: Unseen Companion
A main sequence star with a spectral type of G is found. It has a binary companion star that cannot be
seen, but which has an unknown mass. Which of the following could the companion be?
a) black hole
b) neutron star, or black hole
c) white dwarf, neutron star, or black hole
d) main sequence star, white dwarf, neutron star, or black hole
Your answer:
d) main sequence star, white dwarf, neutron star, or black hole
Your Turn: Unseen Companion
A main sequence star with a spectral type of B7 is found. It has a binary companion star that cannot be
seen, but which has a mass of 15 solar masses. Which of the following could the companion be? Explain
your reasoning.
main sequence star, white dwarf, neutron star, black hole
(Hint: consider the possible masses for each object, whether or not you would be able to see it, and in
the case of the stellar corpses whether it should have had time to evolve that far)
Your answer:
main sequence star; only one within the range of possibility.
main sequence star – 10-20 sm
white dwarf - .015-1.2 sm
neutron star – 1.4 sm
black hole – 3-10 sm
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